Linear equations help

Question

Alberts monthly cell bill is y dollars in terms of number of minutes of talk time x is represented by the equation y=to+b. In particular month he paid $30 for 100 minutes of talk time. In another month, he paid $60 for 250 minutes of talk time. Write the related system of linear equations

Answer 1

y = mx + b where the slope m is the price per minute and b is the flat fee

$30 = m(100) + b

$60 = m(250) + b

subtracting the equations:

60 - 30 = 250m - 100m <-- b cancels out

30 = 150 m

30/150 = m

1/5 = m

so the rate per minute is 1/5 = $0.20 or 20 cents per minute

$30 = (0.2)(100) + b

$30 = 20 + b

b = 10

the flat fee is $10.

Note that $10 + 0.2*250 = $10 + 50 = 60.

the flat fee is $10 and the rate is 20 cents per minute $0.20/min